A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field....

A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field. Before each day of play, we assume that each team has a rating. For example, if the rating for the Bears is + 10 and the rating for the Bengals is +6, we would predict the Bears to beat the Bengals by 10 - 6 = 4 points. Suppose that the Bears play the Bengals and win by 20 points. For this game, we underpredicted the Bears’ performance by 20 - 4 = 16 points. The best
 for pro football is
 0.10. After the game, we therefore increase the Bears’ rating by 16(0.1) = 1.6 and decrease the Bengals’ rating by 1.6 points. In a rematch, the Bears would be favored by (10 + 1.6)- (6 + 1.6) = 7.2 points.


a. How does this approach relate to the equation Lt = Lt1 + Et ?

b. Suppose that the home field advantage in pro football is 3 points; that is, home teams tend to outscore visiting teams by an average of 3 points a game. How could the home field advantage be incorporated into this system?


c. How could we determine the best
 for pro football?


d. How might we determine ratings for each team at the beginning of the season?


e. Suppose we try to apply the previous method to predict pro football (16-game schedule), college football (11-game schedule), college basketball (30-game schedule), and pro basketball (82-game schedule). Which sport would probably have the smallest optimal
? Which sport would probably have the largest optimal
?

f. Why would this approach probably yield poor forecasts for Major League Baseball?